50=-4.9t^2+19.6t+58.8

Solution for 50=-4.9t^2+19.6t+58.8 equation:

50=-4.9t^2+19.6t+58.8

We move all terms to the left:

50-(-4.9t^2+19.6t+58.8)=0

We get rid of parentheses

4.9t^2-19.6t-58.8+50=0

We add all the numbers together, and all the variables

4.9t^2-19.6t-8.8=0

a = 4.9; b = -19.6; c = -8.8;
Δ = b2-4ac
Δ = -19.62-4·4.9·(-8.8)
Δ = 556.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19.6)-\sqrt{556.64}}{2*4.9}=\frac{19.6-\sqrt{556.64}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.6)+\sqrt{556.64}}{2*4.9}=\frac{19.6+\sqrt{556.64}}{9.8}
$